Errr, no. Absolutely not.
I guess you didn't have a map to look at. Its about 150 miles as the crow flies over the Gulf of Suez, but around 600 miles by road through Suez town, Cairo then down the Nile valley. Not on.
go to Makadi bay, you have the beach, the Red Sea, the diving, the 5 star luxury hoptel complex but nearer to luxor, still no where near the pyramids though either
I'm sure some agent could book you on a 4am flight there, and a 10am flight back. And it would cost you �200-300 and you'd be in luxor for an hour or two (max). But you have to ask if that would be worthwhile.
I've been to Egypt several times, and seen people doing Luxor and Cairo side-trips like this. I've always figured that both of these cities are worthy of more time and so have never been...